Scattering Theory of Classical and Quantum N-Particle Systems

1997
ISBN: 978-3-540-62066-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 444 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1810 g

Reihe: Theoretical and Mathematical Physics

A system of N non-relativistic classical particles interacting with pair potentials is described by a Hamiltonian of the form (0.0.1) This Hamiltonian generates a flow ¢(t) on the phase space JR3N x JR3N. An analogous system of N quantum particles is described by a Hamiltonian of the form N 1 H:= -L -Llj + L \lij(Xi - Xj)' (0.0.2) j=l 2mj l$i

Zielgruppe

Research

Autoren/Hrsg.

Gerard, Christian

Derezinski, Jan

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

0. Introduction.- 1. Classical Time-Decaying Forces.- 2. Classical 2-Body Hamiltonians.- 3. Quantum Time-Decaying Hamiltonians.- 4. Quantum 2-Body Hamiltonians.- 5. Classical N-Body Hamiltonians.- 6. Quantum N-Body Hamiltonians.- A. Miscellaneous Results in Real Analysis.- A.1 Some Inequalities.- A.2 The Fixed Point Theorem.- A.3 The Hamilton-Jacobi Equation.- A.4 Construction of Some Cutoff Functions.- A.5 Propagation Estimates.- A.6 Comparison of Two Dynamics.- A.7 Schwartz’s Global Inversion Theorem.- B. Operators on Hilbert Spaces.- B.1 Self-adjoint Operators.- B.2 Convergence of Self-adjoint Operators.- B.3 Time-Dependent Hamiltonians.- B.4 Propagation Estimates.- B.5 Limits of Unitary Operators.- B.6 Schur’s Lemma.- C. Estimates on Functions of Operators.- C.1 Basic Estimates of Commutators.- C.2 Almost-Analytic Extensions.- C.3 Commutator Expansions I.- C.4 Commutator Expansions II.- D. Pseudo-differential and Fourier Integral Operators.- D.0 Introduction.- D.1 Symbols of Operators.- D.2 Phase—Space Correlation Functions.- D.3 Symbols Associated with a Uniform Metric.- D.4 Pseudo-differential Operators Associated with a Uniform Metric.- D.5 Symbols and Operators Depending on a Parameter.- D.6 Weighted Spaces.- D.7 Symbols Associated with Some Non-uniform Metrics.- D.8 Pseudo-differential Operators Associated with the Metric 91.- D.9 Essential Support of Pseudo-differential Operators.- D.10 Ellipticity.- D.12 Non-stationary Phase Method.- D.13 FIO’s Associated with a Uniform Metric.- D.14 FIO’s Depending on a Parameter.- References.